Greece, like some other countries (such as Israel and India) provides that certain "personal status" disputes -- such as those involve family law and the distribution of property at death -- are decided by religious courts of the person's religion. In Greece, this used to apply to Jews and Muslims, but since 1946 applied only to Muslims in a particular province.
Such a rule means that how much you inherit under a will may well depend on the testator's religion. Indeed, Molla Sali's husband left her all his property under a will, and in Greek secular courts that will would be enforced as written; but because he was Muslim, Greek courts concluded that Islamic law applied, and under Islamic law the wife would only get one-quarter of the property, regardless of the will. (The provision was legistlatively made optional in 2018, to be used only when the person expressly agreed, but the Greek proceedings in this case happened before then.)
In Wednesday's decision (Molla Salli v. Greece), the European Court of Human Rights held that this was impermissible religious discrimination:
[Molla Salli], as the beneficiary of a will made in accordance with the Civil Code by a testator of Muslim faith, was in a relevantly similar situation to that of a beneficiary of a will made in accordance with the Civil Code by a non-Muslim testator, and was treated differently on the basis of "other status", namely the testator's religion.
Nor was the court persuaded by the argument that this discrimination was justified because it was called for by treaties that protected the rights of Muslim minorities in Greece and Christian minorities in Turkey; among other things, the court concluded that the treaties didn't require Greece to apply Muslim law.
The court expressly distinguished a situation where choice-of-law rules call for application of foreign law, and the foreign law happens to be based on Islamic law: "In such cases, ... Islamic law is not applied as such but as the law of a (non-European) sovereign State, subject to the requirements of public-policy" (I take it that the last clause refers to the rule that one country will only apply a foreign country's law when the foreign law does not violate the applying country's important public policies).
The court's decision also doesn't deal with religious arbitration under contractual provisions, since rules allowing such arbitration don't themselves involve governmental religious discrimination. And the court didn't have to reach the separate question whether the Greek legal system's application of Islamic property distribution rules would be invalid because those rules discriminate based on sex (since "[m]ale heirs have double the share in the estate as compared with female heirs"). Thanks to Prof. Howard Friedman (Religion Clause) for the pointer.
UPDATE: I changed the first two paragraphs to clarify that the compulsory application of Islamic law was only in force in a particular province, where there is a particularly substantial Muslim population, and also to note that the compulsory nature of the rule was repealed in 2018; thanks to commenter Marinned for reminding me about this.